■サマーヴィルの等面四面体(その431)
n=2rのとき
ρ/l=((2r+1)/8r(r+1))^1/2
をnに戻すと
ρ/l=((n+1)/4n(n/2+1))^1/2
ρ/l=((n+1)/2n(n+2))^1/2
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[1]nが偶数のとき
Σp^2(n−p+1)^2
=n(n+1)(n+2){n^2+2n+2}/60
が正しいとしたら,
k^2・n(n+1)(n+2){n^2+2n+2}/60=(n+1)/2n(n+2)
k^2=30/{n^2+2n+2}
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[2]nが奇数のとき
k^2・Σp^2(n−p+1)^2
=30/{n^2+2n+2}・(n+1)(n−1){8n^3+25n^2+28n+15}/480
=(n+1)(n−1){8n^3+25n^2+28n+15}/16{n^2+2n+2}
n=3を代入すると
8・{216+225+84・15}/16・17
=8・540/16・17 (NG)
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